Question

Write the general form of the equation which matches the graph below. In complete sentences, explain the process taken to find this equation

Answer 1

ur having a bad day with parabolas arent you?? lol

Answer 2

yes i am its like the only thing i dont understand :(

Answer 3

whats the dashed line represent any idea??

Answer 4

the directrix

Answer 5

ok cool. its simple. firstly u notice its an inverted parabola??

Answer 6

whats an inverted parabola?

Answer 7

well its upside down....

Answer 8

oh okay so then yeah lol

Answer 9

so doesnt that means it will be negative

Answer 10

so the general equation of a parabola is y=ax^2. are you aware of this?

Answer 11

yes. it will be negative and become y= -ax^2

Answer 12

yes i know the equation just dont no how to write it just by looking at the graph

Answer 13

wait i thought the equation would be y=a(x-h)^2+k since its away from the vertex

Answer 14

but thats not all. you have a particular vertex and directrix of this parabola. so the equation becomes\[(x-h)^{2}=4*p*(y-k)\] where (h.k) is the focus and p is the distance from the vertex to the focus and the vertex to the directrix. you can see this distance to be equal?? (4)

Answer 15

yeah ur right

Answer 16

u forgot to include the y coordinates' shift like u did with the x...

Answer 17

oh okay i think i got that

Answer 18

cool..

Answer 19

but how do i write the equation

Answer 20

simple. h=3. and k= -4. so put that in the equation i wrote along with p=4. there is ur equation.

Answer 21

so i have a question is the parabola at the origin or away from the origin?

Answer 22

away from clearly....if its vertex lies at the origin, then u say it is at the origin. but u can see its not.

Answer 23

so the origin is 0,0 right

Answer 24

so since its at (3,1) its away correct?

Answer 25

yup :)

Answer 26

oh okay got it now

Answer 27

so would the focus be (3,-4)

Answer 28

yup....correction, the vertex is at (3,0) not (3,1). but the focus is at (3,-4). yup

Answer 29

by bad typo thats what i have written down

Answer 30

lol...happens

Answer 31

yeah